3x+25=2x^2+14x-15

Solution for 3x+25=2x^2+14x-15 equation:

3x+25=2x^2+14x-15

We move all terms to the left:

3x+25-(2x^2+14x-15)=0

We get rid of parentheses

-2x^2+3x-14x+15+25=0

We add all the numbers together, and all the variables

-2x^2-11x+40=0

a = -2; b = -11; c = +40;
Δ = b2-4ac
Δ = -112-4·(-2)·40
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-21}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+21}{2*-2}=\frac{32}{-4}
=-8
$